This is relatively easy to do. The shape of the graph is determined entirely by the coeffiecients and the squared terms.

If there is an x^{2} term **and** a y^{2} term (on the same side of the equation) and the two coeffiecients are equal, then the graph is a circle.

If there is an x^{2} term **and** a y^{2} term (on the same side of the equation) and the two coeffiecients are **not** equal, then the graph is an ellipse.

If there is only an x^{2} term **or** a y^{2} regardless of the coeffiecients, the graph is a parabola.

If there is an x^{2} **and** a y^{2} term on the same side of the equation and one term is negative, the graph is a hyperbola.